TY  - Type of reference 
TI  - [FORTHCOMING] Réseaux dans les groupes nilpotents métabéliens de type ℝ<sup>n</sup> ⋊ ℝ<sup>m</sup> 
AU  - Béchir Dali 
 
AU  - Yasmin Ben Soula 
AB  - The main objective of this paper is  to characterize a class of lattices, called splittable lattices, in the nilpotent semidirect product Lie group $$$G=\mathbb R^n\rtimes_\eta\mathbb R^m$$$. Here, $$$\eta$$$ denotes the representation of the abelian Lie group $$$\mathbb R^m$$$ in $$$GL_n(\mathbb R)$$$ defined by $$$\eta(t_{1},\dots,t_{m})=\exp{(\sum_{i=1}^mt_iN_i)}$$$ with $$$(N_i)_{1\leq i\leq m}$$$ is a set of pairwise commuting nilpotent matrices in $$$\mathbb Q^{n\times n}$$$. As an application we study the case of the nilpotent Lie group $$$F_{n,m}=\mathbb R^n\rtimes_\eta\mathbb R^m$$$ where $$$N_i=J^i$$$ with $$$J=\sum_{k=1}^{n-1}E_{k+1,k}$$$ where $$$E_{k+1,k}\in\mathbb R^{n\times n}$$$ denotes the matrix given by the Kronecker delta, namely,   $$$\big(E_{k+1,k}\big)_{i,j}=\delta_{i,k+1}\delta_{j,k}$$$. 
DO  - À venir 
JF  - Avancées en Mathématiques Pures et Appliquées 
KW  - lattice, nilpotent Lie group, metabelian group, exponential mapping, lattice, nilpotent Lie group, metabelian group, exponential mapping,  
L1  -  
LA  - fr 
PB  - ISTE OpenScience 
DA  - 2026/07/22 
SN  - 1869-6090 
TT  - [FORTHCOMING] Lattices in the metabelian nilpotent Lie group ℝ<sup>n</sup> ⋊ ℝ<sup>m</sup> 
UR  - https://www.openscience.fr/Reseaux-dans-les-groupes-nilpotents-metabeliens-de-type-%E2%84%9Dn-%E2%8B%8A-%E2%84%9Dm 
IS  - Articles à paraître<br> 
VL  -  
ER  -